In this paper, we present parallel implementations of two methods for computing turbulent flow in complex geometries.Both methods are based on the random vortex method, which is particularly suited for computing complex, viscous, incompressible flow across a wide range of flow regimes and characteristics.The lirst method is a full vortex method, designed to accurately simulate such fluid phenomenon as vortex shedding, merger, and rollup, as well quantitative features of the flow.The second method, based on a "vortexin-cell" method, is an extremely fast version which can offer qualitative portrayal of the dominant fluid structures and mechanisms useful in the design stage.Both methods are non-standard, containing few of the positive attributes commonly associated with methods that easily lend themselves to massively parallel implementations.They are Lagrangian schemes, in which the position of each computational element is affeeted by all others at each time step.The efficient execution of these methods on a Connection Machine CM-2 requires parallel N-body solvers, parallel elliptic solvers, and pamllel data structures for the adaptive creation of computational elements on the boundary of the confining region.provide timing runs.Both are connected to the Realtime Interactive Visualization Environment described in [10].

The authors have designed and implemented a hypercube algorithm for direct N-body solvers on the Connection Machine CM-2. The algorithm is optimal in the sense that, as long as there is sufficient data, it uses the full communication bandwidth of a hypercube of any dimension. When the number of bodies per node is large enough, the communication time for the implementation is negligible, i.e., less than 2%. In particular, this means that one obtains close to optimal speedup in the regime. To obtain this performance, 'rotated and translated Gray codes' which result in time-wise edge disjoint Hamiltonian paths on the hypercube are used. Timings are presented for a collection of interacting point vortices in two dimensions. The computation of the velocities of 14,000 vortices in 32-bit precision takes 2 seconds on a 16K CM-2.>